Vol. 54, No. 4, pp. 407-420 (1997)
On an Analogue of Completely Multiplicative Functions
Pentti Haukkanen and Pia RuokonenDepartment of Mathematical Sciences, University of Tampere,
P.O. Box 607, FIN-33101 Tampere - FINLAND
Abstract: We introduce exponentially $A$-multiplicative functions which serve as an analogue of completely multiplicative functions in the setting of exponential $A$-convolu\-tion, where $A$ is Narkiewicz's regular convolution. We show that exponentially $A$-multi\-plicative functions under exponential $A$-convolution possess properties similar to the familiar properties of completely multiplicative functions under the Dirichlet convolution.
Keywords: Exponential convolution; Narkiewicz's regular convolution; completely multiplicative functions; characterizations; functional equations.
Classification (MSC2000): 11A25
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Electronic version published on: 29 Mar 2001. This page was last modified: 27 Nov 2007.